The geometric sequence $(a_i)$ is defined by the formula: $a_i = -\dfrac{8}{3} \left(\dfrac{3}{4}\right)^{i - 1}$ What is $a_{4}$, the fourth term in the sequence?
Solution: From the given formula, we can see that the first term of the sequence is $-\dfrac{8}{3}$ and the common ratio is $\dfrac{3}{4}$ To find $a_{4}$ , we can simply substitute $i = 4$ into the given formula. Therefore, the fourth term is equal to $a_{4} = -\dfrac{8}{3} \left(\dfrac{3}{4}\right)^{4 - 1} = -\dfrac{9}{8}$.